# Math : Trigonometry

## Contents for Trigonometry Module 2 : Trigonometric Functions and Identities## Values of Trigonometric Functions for Common AnglesIt is useful to know the values of the trigonometric functions for certain common angles. The values of the trigonometric functions for angles 0, 30^{o}, 45^{o}, 60^{o} and 90^{o} are given in the table below.
It is possible to obtain the values in the above table for 0, 45
The values in the above table can be easily remembered using the following mnemonic. The values of sin 0, sin 30 ## Important Trigonometric IdentitiesSome important trigonometric identities relating functions of a single angle (say, A) are given below.
These identities are useful in simplification and solution of problems. Their proofs are given below. - Based on the right-angled triangle in the figure alongside, sin
*A*= a / b and cos*A*= c / b. Therefore sin^{2}*A*+ cos^{2}*A*= (a^{2}+ c^{2})/b^{2}. By Pythagoras Theorem, a^{2}+ c^{2}= b^{2}in a right-angled triangle. Thus**sin**and equation (1) is proved.^{2}*A*+ cos^{2}*A*= 1 - On dividing both sides of equation (1) by cos
^{2}*A*, we obtain**tan**. Equation (2) is proved.^{2}*A*+ 1 = 1 / cos^{2}*A*= sec^{2}*A* - On dividing both sides of equation (1) by sin
^{2}*A*, we obtain**1 + cot**. Equation (3) is proved.^{2}*A*= 1/sin^{2}*A*= cosec^{2}*A*
## Cofunction PropertyThe cofunction property is very important and is given below.
The cofunction property is easy to prove by starting with the fact that the sum of the three angles of a triangle is always 180 - sin (90
^{o}-*A*) = sin*C*= c / b = cos*A* - cos (90
^{o}-*A*) = cos*C*= a / b = sin*A* - tan (90
^{o}-*A*) = tan*C*= c / a = cot*A*
Practice Exercise for Trigonometry Module 2: Trigonometric Functions and Identities |